Swan-Tate cohomology of meromorphic circle actions

Abstract

We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology $t_\T E$ of a complex-oriented $E_{\infty }$ ring-spectrum $E$ is the extension of a Hopf algebra by its dual, which provides an algebraic rigidification of geometric interest. This note reviews the cases $E=H,K$ and $MU$, with special attention to $\lambda$-ring structures.

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